Finite Group Databasebeta

← C67×#14042 #30693293

Subgroups — C67×#14042 #30693293

Order 17152.

1442 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C67C211yesmaximal, characteristic
2C2×#387×C67C212yesmaximal
3C2×C4×C4⋊C4×C67C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C67C211yesmaximal, characteristic
5C67×#1443C212yesmaximal
6C67×#1441C212yesmaximal
7C67×C4⋊#95C211yesmaximal, characteristic
8C67×C4⋊#95C211yesmaximal, characteristic
9C67×C4⋊#95C211yesmaximal, characteristic
10C67×C4⋊#95C211yesmaximal, characteristic
11C67×#1434C212yesmaximal
12C22×C4⋊C4×C67C2211yescharacteristic
13C22×C4⋊C4×C67C2211yescharacteristic
14C22×C4⋊C4×C67C2211yescharacteristic
15C22×C4⋊C4×C67C2212yes—
16C22×C4⋊C4×C67C2211yescharacteristic
17C22×C4⋊C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C42×C67C2212yes—
20C22×C42×C67C2211yescharacteristic
21C22×C42×C67C2211yescharacteristic
22C22×C42×C67C2211yescharacteristic
23#389×C67C418yescomplemented
24#387×C67—28no—
25C4×C4⋊C4×C67—24no—
26C4×C4⋊C4×C67—24no—
27C2×#95×C67C2211yescharacteristic
28C2×#95×C67C2212yes—
29C2×#95×C67C2211yescharacteristic
30C2×#95×C67C2212yes—
31C2×#95×C67C2212yes—
32C2×#95×C67C2212yes—
33C2×#95×C67C2212yes—
34C2×#95×C67C2212yes—
35C2×#95×C67C2212yes—
36C2×#95×C67C2212yes—
37C2×#95×C67C2212yes—
38C2×#95×C67C2212yes—
39C23×C4×C67C2312yes—
40C23×C4×C67C2312yes—
41C23×C4×C67C2311yescharacteristic
42C23×C4×C67C2312yes—
43C23×C4×C67C2311yescharacteristic
44C23×C4×C67C2311yescharacteristic
45C23×C4×C67C2312yes—
46C23×C4×C67C2311yescharacteristic
47C23×C4×C67C2311yescharacteristic
48C23×C4×C67C2311yescharacteristic
49C23×C4×C67C2311yescharacteristic
50C2×C4⋊C4×C67—22no—
51C2×C4⋊C4×C67—22no—
52C2×C4⋊C4×C67—22no—
53C2×C4⋊C4×C67—22no—
54C2×C4⋊C4×C67—24no—
55C2×C4⋊C4×C67—22no—
56C2×C4⋊C4×C67—22no—
57C2×C4⋊C4×C67—22no—
58C2×C4⋊C4×C67—22no—
59C2×C4⋊C4×C67—24no—
60C2×C4⋊C4×C67—22no—
61C2×C4⋊C4×C67—22no—
62C2×C4⋊C4×C67—22no—
63C2×C4⋊C4×C67—22no—
64C2×C4⋊C4×C67—22no—
65C2×C4⋊C4×C67—22no—
66C2×C4⋊C4×C67C2×C414yes—
67C2×C4⋊C4×C67C2×C418yes—
68C2×C4⋊C4×C67C2×C414yes—
69C2×C4⋊C4×C67D414yes—
70C2×C4⋊C4×C67Q814yes—
71C2×C42×C67—22no—
72C2×C42×C67—22no—
73C2×C42×C67—22no—
74C2×C42×C67—22no—
75C2×C42×C67—24no—
76C2×C42×C67—22no—
77C2×C42×C67—24no—
78C2×C42×C67—24no—
79C2×C42×C67—22no—
80C2×C42×C67—22no—
81C2×C42×C67C2×C414yes—
82C2×C42×C67D414yes—
83#95×C67—24no—
84#95×C67—22no—
85#95×C67—22no—
86#95×C67—24no—
87#95×C67—24no—
88#95×C67—24no—
89#95×C67—24no—
90#95×C67—24no—
91#95×C67—42no—
92#95×C67—42no—
93#95×C67—42no—
94#95×C67C2×C418yes—
95C24×C67C2411yescharacteristic
96C22×C4×C67—21no—
97C22×C4×C67—21no—
98C22×C4×C67—21no—
99C22×C4×C67—21no—
100C22×C4×C67—21no—
101C22×C4×C67—21no—
102C22×C4×C67—21no—
103C22×C4×C67—21no—
104C22×C4×C67—22no—
105C22×C4×C67—22no—
106C22×C4×C67—21no—
107C22×C4×C67—22no—
108C22×C4×C67—21no—
109C22×C4×C67—21no—
110C22×C4×C67—22no—
111C22×C4×C67—22no—
112C22×C4×C67—21no—
113C22×C4×C67—22no—
114C22×C4×C67—21no—
115C22×C4×C67—21no—
116C22×C4×C67—21no—
117C22×C4×C67—21no—
118C22×C4×C67—21no—
119C22×C4×C67—21no—
120C22×C4×C67—22no—
121C22×C4×C67—22no—
122C22×C4×C67—22no—
123C22×C4×C67—22no—
124C22×C4×C67—22no—
125C22×C4×C67—22no—
126C22×C4×C67—21no—
127C22×C4×C67—22no—
128C22×C4×C67—21no—
129C22×C4×C67—21no—
130C22×C4×C67—21no—
131C22×C4×C67—22no—
132C22×C4×C67—21no—
133C22×C4×C67—22no—
134C22×C4×C67—21no—
135C22×C4×C67—21no—
136C22×C4×C67—22no—
137C22×C4×C67—21no—
138C22×C4×C67—21no—
139C22×C4×C67—21no—
140C22×C4×C67—22no—
141C22×C4×C67—21no—
142C22×C4×C67—21no—
143C22×C4×C67—21no—
144C22×C4×C67—22no—
145C22×C4×C67—21no—
146C22×C4×C67—22no—
147C22×C4×C67—22no—
148C22×C4×C67—22no—
149C22×C4×C67—22no—
150C22×C4×C67—22no—
151C22×C4×C67—22no—
152C22×C4×C67—22no—
153C22×C4×C67C22×C412yes—
154C22×C4×C67C22×C414yes—
155C22×C4×C67C22×C414yes—
156C22×C4×C67C22×C412yes—
157C22×C4×C67C22×C412yes—
158C22×C4×C67C2×D412yes—
159C22×C4×C67C2×D412yes—
160C22×C4×C67C2×D412yes—
161C22×C4×C67C2×D412yes—
162C22×C4×C67C2×D412yes—
163C22×C4×C67C2×D412yes—
164C22×C4×C67C2×Q814yes—
165C22×C4×C67C2×Q812yes—
166C22×C4×C67#4112yes—
167C22×C4×C67#4112yes—
168C22×C4×C67#4112yes—
169C22×C4×C67#4112yes—
170C22×C4×C67#4112yes—
171C22×C4×C67#4112yes—
172C22×C4×C67#4112yes—
173C4⋊C4×C67—28no—
174C4⋊C4×C67—28no—
175C4⋊C4×C67—216no—
176C4⋊C4×C67—28no—
177C4⋊C4×C67—28no—
178C4⋊C4×C67—28no—
179C4⋊C4×C67—44no—
180C42×C67—28no—
181C42×C67—28no—
182C42×C67—48no—
183C42×C67—44no—
184C23×C67C23×C411yescharacteristic
185C23×C67C22×D411yescharacteristic
186C23×C67C22×D411yescharacteristic
187C23×C67C22×Q811yescharacteristic
188C23×C67C2×#4111yescharacteristic
189C23×C67C2×#4111yescharacteristic
190C23×C67C2×#4111yescharacteristic
191C23×C67C2×#4111yescharacteristic
192C23×C67C2×#4111yescharacteristic
193C23×C67C2×#4111yescharacteristic
194C23×C67C2×#4111yescharacteristic
195C23×C67H(5,𝔽2)11yescharacteristic
196C23×C672−1+411yescharacteristic
197C23×C672−1+411yescharacteristic
198C23×C672−1+411yescharacteristic
199C2×C4×C67—22no—
200C2×C4×C67—22no—
201C2×C4×C67—22no—
202C2×C4×C67—22no—
203C2×C4×C67—22no—
204C2×C4×C67—22no—
205C2×C4×C67—22no—
206C2×C4×C67—22no—
207C2×C4×C67—22no—
208C2×C4×C67—22no—
209C2×C4×C67—22no—
210C2×C4×C67—22no—
211C2×C4×C67—24no—
212C2×C4×C67—22no—
213C2×C4×C67—24no—
214C2×C4×C67—24no—
215C2×C4×C67—24no—
216C2×C4×C67—24no—
217C2×C4×C67—22no—
218C2×C4×C67—22no—
219C2×C4×C67—24no—
220C2×C4×C67—22no—
221C2×C4×C67—24no—
222C2×C4×C67—22no—
223C2×C4×C67—22no—
224C2×C4×C67—22no—
225C2×C4×C67—22no—
226C2×C4×C67—22no—
227C2×C4×C67—22no—
228C2×C4×C67—24no—
229C2×C4×C67—22no—
230C2×C4×C67—22no—
231C2×C4×C67—24no—
232C2×C4×C67—42no—
233C2×C4×C67—42no—
234C2×C4×C67—41no—
235C2×C4×C67—41no—
236C2×C4×C67—42no—
237C2×C4×C67—42no—
238C2×C4×C67—42no—
239C2×C4×C67—41no—
240C2×C4×C67—41no—
241C2×C4×C67—41no—
242C2×C4×C67—41no—
243C2×C4×C67—42no—
244C2×C4×C67—41no—
245C2×C4×C67—41no—
246C2×C4×C67—42no—
247C2×C4×C67—42no—
248C2×C4×C67—42no—
249C2×C4×C67—41no—
250C2×C4×C67—41no—
251C2×C4×C67—41no—
252C2×C4×C67—41no—
253C2×C4×C67—42no—
254C2×C4×C67—41no—
255C2×C4×C67—41no—
256C2×C4×C67—42no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—42no—
260C2×C4×C67—42no—
261C2×C4×C67—42no—
262C2×C4×C67—42no—
263C2×C4×C67—42no—
264C2×C4×C67—42no—
265C2×C4×C67—42no—
266C2×C4×C67—42no—
267C2×C4×C67#11714yes—
268C2×C4×C67C4×D414yes—
269C2×C4×C67C4×D414yes—
270C2×C4×C67C4×Q814yes—
271C2×C4×C67#12114yes—
272C2×C4×C67C22⋊Q814yes—
273C2×C4×C67#12314yes—
274C2×C4×C67#12514yes—
275C2×C4×C67#12614yes—
276C22×C67C2×#11711yescharacteristic
277C22×C67C2×C4×D411yescharacteristic
278C22×C67C2×C4×D411yescharacteristic
279C22×C67C2×C4×Q811yescharacteristic
280C22×C67C4×#4111yescharacteristic
281C22×C67#51911yescharacteristic
282C22×C67#52011yescharacteristic
283C22×C67C2×#12111yescharacteristic
284C22×C67C2×C22⋊Q811yescharacteristic
285C22×C67C2×#12311yescharacteristic
286C22×C67#52511yescharacteristic
287C22×C67C2×#12511yescharacteristic
288C22×C67C2×#12611yescharacteristic
289C22×C67#52911yescharacteristic
290C22×C67#53211yescharacteristic
291C22×C67#53611yescharacteristic
292C22×C67#53711yescharacteristic
293C22×C67#54111yescharacteristic
294C22×C67#54211yescharacteristic
295C22×C67#54711yescharacteristic
296C22×C67#54711yescharacteristic
297C22×C67D4×Q811yescharacteristic
298C22×C67#55011yescharacteristic
299C22×C67#55211yescharacteristic
300C22×C67#55211yescharacteristic
301C22×C67#55211yescharacteristic
302C22×C67#55311yescharacteristic
303C22×C67#55411yescharacteristic
304C22×C67#55511yescharacteristic
305C22×C67#55611yescharacteristic
306C22×C67#55611yescharacteristic
307C22×C67#55611yescharacteristic
308C22×C67#55611yescharacteristic
309C22×C67#55711yescharacteristic
310C22×C67#55711yescharacteristic
311C4×C67—24no—
312C4×C67—24no—
313C4×C67—42no—
314C4×C67—44no—
315C4×C67—42no—
316C4×C67—42no—
317C4×C67—42no—
318C4×C67—44no—
319C4×C67—44no—
320C4×C67—82no—
321C4×C67#38718yescomplemented
322#14042C6711yesmaximal, characteristic, direct product factor, Sylow
323C2×C67C2×#38711yescharacteristic
324C2×C67C4×#12111yescharacteristic
325C2×C67#232311yescharacteristic
326C2×C67#235411yescharacteristic
327C2×C67#235611yescharacteristic
328C2×C67#236511yescharacteristic
329C2×C67#237011yescharacteristic
330C2×C67#248511yescharacteristic
331C2×C67#248611yescharacteristic
332C2×C67#250611yescharacteristic
333C2×C67#250811yescharacteristic
334C2×C67#251211yescharacteristic
335C2×C67#251411yescharacteristic
336C2×C67#253811yescharacteristic
337C2×C67#258111yescharacteristic
338C2×#389C2×C6711yescharacteristic
339C2×#387C2×C6712yes—
340C2×C4×C4⋊C4C2×C6711yescharacteristic
341C2×C4×C4⋊C4C2×C6711yescharacteristic
342#1443C2×C6712yes—
343#1441C2×C6712yes—
344C4⋊#95C2×C6711yescharacteristic
345C4⋊#95C2×C6711yescharacteristic
346C4⋊#95C2×C6711yescharacteristic
347C4⋊#95C2×C6711yescharacteristic
348#1434C2×C6712yes—
349C67#1404211yescharacteristic, direct product factor, Sylow
350C22×C4⋊C4C22×C6711yescharacteristic
351C22×C4⋊C4C22×C6711yescharacteristic
352C22×C4⋊C4C22×C6711yescharacteristic
353C22×C4⋊C4C22×C6711yescharacteristic
354C22×C4⋊C4C22×C6712yes—
355C22×C4⋊C4C22×C6711yescharacteristic
356C22×C4⋊C4C22×C6711yescharacteristic
357C22×C42C22×C6712yes—
358C22×C42C22×C6711yescharacteristic
359C22×C42C22×C6711yescharacteristic
360C22×C42C22×C6711yescharacteristic
361#389C4×C6718yescomplemented
362#387—28no—
363C4×C4⋊C4—24no—
364C4×C4⋊C4—24no—
365C2×#95C22×C6711yescharacteristic
366C2×#95C22×C6712yes—
367C2×#95C22×C6712yes—
368C2×#95C22×C6712yes—
369C2×#95C22×C6712yes—
370C2×#95C22×C6712yes—
371C2×#95C22×C6712yes—
372C2×#95C22×C6711yescharacteristic
373C2×#95C22×C6712yes—
374C2×#95C22×C6712yes—
375C2×#95C22×C6712yes—
376C2×#95C22×C6712yes—
377C23×C4C23×C6712yes—
378C23×C4C23×C6712yes—
379C23×C4C23×C6712yes—
380C23×C4C23×C6711yescharacteristic
381C23×C4C23×C6711yescharacteristic
382C23×C4C23×C6711yescharacteristic
383C23×C4C23×C6712yes—
384C23×C4C23×C6711yescharacteristic
385C23×C4C23×C6711yescharacteristic
386C23×C4C23×C6711yescharacteristic
387C23×C4C23×C6711yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4C2×C4×C6714yes—
405C2×C4⋊C4C2×C4×C6718yes—
406C2×C4⋊C4C2×C4×C6714yes—
407C2×C4⋊C4D4×C6714yes—
408C2×C4⋊C4Q8×C6714yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×C4×C6714yes—
420C2×C42D4×C6714yes—
421#95—22no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95C2×C4×C6718yes—
433C24C24×C6711yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4C22×C4×C6712yes—
492C22×C4C22×C4×C6714yes—
493C22×C4C22×C4×C6714yes—
494C22×C4C22×C4×C6712yes—
495C22×C4C22×C4×C6712yes—
496C22×C4C2×D4×C6712yes—
497C22×C4C2×D4×C6712yes—
498C22×C4C2×D4×C6712yes—
499C22×C4C2×D4×C6712yes—
500C22×C4C2×D4×C6712yes—
501C22×C4C2×D4×C6712yes—
502C22×C4C2×Q8×C6714yes—
503C22×C4C2×Q8×C6712yes—
504C22×C4#41×C6712yes—
505C22×C4#41×C6712yes—
506C22×C4#41×C6712yes—
507C22×C4#41×C6712yes—
508C22×C4#41×C6712yes—
509C22×C4#41×C6712yes—
510C22×C4#41×C6712yes—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—216no—
514C4⋊C4—28no—
515C4⋊C4—28no—
516C4⋊C4—28no—
517C4⋊C4—44no—
518C42—28no—
519C42—28no—
520C42—48no—
521C42—44no—
522C23C23×C4×C6711yescharacteristic
523C23C22×D4×C6711yescharacteristic
524C23C22×D4×C6711yescharacteristic
525C23C22×Q8×C6711yescharacteristic
526C23C2×#41×C6711yescharacteristic
527C23C2×#41×C6711yescharacteristic
528C23C2×#41×C6711yescharacteristic
529C23C2×#41×C6711yescharacteristic
530C23C2×#41×C6711yescharacteristic
531C23C2×#41×C6711yescharacteristic
532C23C2×#41×C6711yescharacteristic
533C23H(5,𝔽2)×C6711yescharacteristic
534C232−1+4×C6711yescharacteristic
535C232−1+4×C6711yescharacteristic
536C232−1+4×C6711yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4#117×C6714yes—
606C2×C4C4×D4×C6714yes—
607C2×C4C4×D4×C6714yes—
608C2×C4C4×Q8×C6714yes—
609C2×C4#121×C6714yes—
610C2×C4C22⋊Q8×C6714yes—
611C2×C4#123×C6714yes—
612C2×C4#125×C6714yes—
613C2×C4#126×C6714yes—
614C22C2×#117×C6711yescharacteristic
615C22C2×C4×D4×C6711yescharacteristic
616C22C2×C4×D4×C6711yescharacteristic
617C22C2×C4×Q8×C6711yescharacteristic
618C22C4×#41×C6711yescharacteristic
619C22#519×C6711yescharacteristic
620C22#520×C6711yescharacteristic
621C22C2×#121×C6711yescharacteristic
622C22C2×C22⋊Q8×C6711yescharacteristic
623C22C2×#123×C6711yescharacteristic
624C22#525×C6711yescharacteristic
625C22C2×#125×C6711yescharacteristic
626C22C2×#126×C6711yescharacteristic
627C22#529×C6711yescharacteristic
628C22#532×C6711yescharacteristic
629C22#536×C6711yescharacteristic
630C22#537×C6711yescharacteristic
631C22#541×C6711yescharacteristic
632C22#542×C6711yescharacteristic
633C22#547×C6711yescharacteristic
634C22#547×C6711yescharacteristic
635C22D4×Q8×C6711yescharacteristic
636C22#550×C6711yescharacteristic
637C22#552×C6711yescharacteristic
638C22#552×C6711yescharacteristic
639C22#552×C6711yescharacteristic
640C22#553×C6711yescharacteristic
641C22#554×C6711yescharacteristic
642C22#555×C6711yescharacteristic
643C22#556×C6711yescharacteristic
644C22#556×C6711yescharacteristic
645C22#556×C6711yescharacteristic
646C22#556×C6711yescharacteristic
647C22#557×C6711yescharacteristic
648C22#557×C6711yescharacteristic
649C4—24no—
650C4—24no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—82no—
659C4#387×C6718yescomplemented
660C2C2×#387×C6711yescharacteristic
661C2C4×#121×C6711yescharacteristic
662C2C67×#232311yescharacteristic
663C2C67×#235411yescharacteristic
664C2C67×#235611yescharacteristic
665C2C67×#236511yescharacteristic
666C2C67×#237011yescharacteristic
667C2C67×#248511yescharacteristic
668C2C67×#248611yescharacteristic
669C2C67×#250611yescharacteristic
670C2C67×#250811yescharacteristic
671C2C67×#251211yescharacteristic
672C2C67×#251411yescharacteristic
673C2C67×#253811yescharacteristic
674C2C67×#258111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C67C24
commutatorC23C23×C4×C67
Frattini, cosocleC24C24×C67
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
23. #389×C67C4semidirect
321. C4×C67#387semidirect
322. #14042C67direct (N × H)
349. C67#14042direct (N × H)
361. #389C4×C67semidirect
659. C4#387×C67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#389×C672
C2×#387×C672
C2×C4×C4⋊C4×C672
C67×#14432
C67×#14412
C67×C4⋊#952
C67×#14342
#1404267